In this Section, we focus on the leading operator \( {C_4 \over M_{\rm Pl}^2}\,\phi ^4 s^2\)  and compute the resulting DM relic abundance in the resonant regime, \(C_4 \phi _0^4 /M_{\rm Pl}^2 \gg m_\phi ^2\) ,
assuming \(m_\phi \gg m_s\) . As explained above, the analytical approach to resonant particle production has significant limitations,
given the complexity of the Whittaker–Hill equation as well as backreaction and rescattering effects. Therefore, we resort to lattice simulations using the numerical tool CosmoLattice [1]}, [2]}.
